What do the following two equations represent? $4x+3y = 5$ $12x+9y = 5$
Putting the first equation in $y = mx + b$ form gives: $4x+3y = 5$ $3y = -4x+5$ $y = -\dfrac{4}{3}x + \dfrac{5}{3}$ Putting the second equation in $y = mx + b$ form gives: $12x+9y = 5$ $9y = -12x+5$ $y = -\dfrac{4}{3}x + \dfrac{5}{9}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.